A sensor which provides an accumulated or integrated value of a physical input typically outputs a digital value which is expressed as a binary counter. This digital value changes when the physical quantity changes and roll-over occurs when the physical quantity exceeds a maximum or minimum value of the digital value. In order to calculate a physical value from the accumulative digital output provided by such a sensor, a counter increment, which is a difference between a current digital output value and a previous digital output value, and a data acquisition period (or a sampling frequency, which is a reciprocal of the data acquisition period), which is a time interval between the two values, are used. In this case, when an absolute value of the counter increment is greater than a half of the maximum value that the binary counter can have, a sign of the calculated physical value is changed and thus a measurement value cannot be exactly calculated. Therefore, the absolute value of the counter increment which is the difference between the current output value and the previous output value should always be smaller than the half of the maximum value of the binary counter. That is, even when the sensor itself is able to measure a greater value, a physical quantity corresponding to the half of the counter maximum value is the maximum measurement value that can be calculated using this sensor due to the limited size of the binary counter (or the limited number of binary bits). In order to increase the maximum measurement value, the maximum value (the number of binary bits) of the counter should be increased or the sampling frequency should be increased. However, this may increase the cost of the sensor and complexity of a system using the sensor. Korean Patent Publication No. 10-2009-0068172 discloses a signal processing device for converting an output from a sensor into a digital value.